Question: Simplify; express your answer in exponential form. Assume $p\neq 0, q\neq 0$. $\dfrac{{p^{3}q^{-2}}}{{(p^{-3}q^{5})^{-4}}}$
To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${p^{3}q^{-2} = p^{3}q^{-2}}$ On the left, we have ${p^{3}}$ to the exponent ${1}$ . Now ${3 \times 1 = 3}$ , so ${p^{3} = p^{3}}$ Apply the ideas above to simplify the equation. $\dfrac{{p^{3}q^{-2}}}{{(p^{-3}q^{5})^{-4}}} = \dfrac{{p^{3}q^{-2}}}{{p^{12}q^{-20}}}$ Break up the equation by variable and simplify. $\dfrac{{p^{3}q^{-2}}}{{p^{12}q^{-20}}} = \dfrac{{p^{3}}}{{p^{12}}} \cdot \dfrac{{q^{-2}}}{{q^{-20}}} = p^{{3} - {12}} \cdot q^{{-2} - {(-20)}} = p^{-9}q^{18}$